We give a denotational semantics for a region-based effect system that supports type abstraction in the sense that only externally visible effects need to be tracked: non-observable internal modifi- cations, such as the reorganisation of a search tree or lazy initialisation, can count as \u2018pure\u2019 or \u2018read only\u2019. This \u2018fictional purity\u2019 allows clients of a module to validate soundly more effect-based program equivalences than would be possible with previous semantics. Our semantics uses a novel variant of logical relations that maps types not merely to partial equivalence relations on values, as is commonly done, but rather to a proof-relevant generalisation thereof, namely setoids. The objects of a setoid establish that values inhabit semantic types, whilst its morphisms are understood as proofs of semantic equivalence. The transition to proof-relevance solves two awkward problems caused by na\u00a8\u0131ve use of existential quantification in Kripke logical relations, namely failure of admissibility and spurious functional dependencies.<\/p>\n","protected":false},"excerpt":{"rendered":"
We give a denotational semantics for a region-based effect system that supports type abstraction in the sense that only externally visible effects need to be tracked: non-observable internal modifi- cations, such as the reorganisation of a search tree or lazy initialisation, can count as \u2018pure\u2019 or \u2018read only\u2019. 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